ENTRANCE EXAMINATION FOR THE BACHELOR OF ENGINEERING DEGREE PROGRAMMES

ENTRANCE EXAMINATION FOR THE BACHELOR OF ENGINEERING DEGREE PROGRAMMES INSTRUCTIONS The Entrance Examination consists of three parts: Problem Solving (Part 1), Questions on Motivation (Part ), English Language Test: Essay (Part 3). PLEASE NOTE THE FOLLOWING: 1. The following parts of the examination are compulsory for all: Part 1 Problem Solving Part Questions on Motivation. The English Language Test (Part 3) is compulsory only for those who do not have exemption from it, as stated in the application requirements. 3. The duration of the examination Parts 1 and is h 30 min. The duration of Part 3, the English Language Test, is 60 min. 4. All the answers must be written in the spaces indicated in the tasks. Answers written on any other sheets will not be assessed. 5. You will also get an additional sheet to make your own notes and calculations on. This sheet also has to be returned, but it will not influence the assessment. PLEASE DO NOT TURN THE PAGE UNTIL YOU ARE GIVEN PERMISSION.

1 3 4 5 6 7 8 9 10 Do not fill this table! Part 1, section A, page 1/x Part 1, section A: PROBLEM SOLVING, MATHEMATICS The mathematical part of the exam consists of xxxx problems in mathematics. Please answer in the space reserved for each task. The main ideas of the calculations must be shown. FAMILY NAME AND FIRST NAME(S): APPLICATION NUMBER: DATE OF BIRTH: APPLICATION OPTIONS: Civil Engineering Information Technology Media Engineering PROBLEMS: 1. Simplify the expressions. 3 3 a) 5 3 3 b) 4ln x 6ln x 1/ c) 3x 6 x 1. x 3x x 8. Solve the equations. a) 1 1 t t b) x 1 x 1 1 x 1 x. c) cos 3 0 1

Part 1, section A, page /x 3. Solve the following inequalities. 3 x a) x 1 b) 3x 1 1 3 c) x 3 x 4. The product of two numbers is 30 and the average 6. What are these numbers? 5. Consider two straight lines L1 (y = x +1) and L (y=x). a) What is the slope of line L1 in respect to line L? b) What is the equation of line L1 in respect to line L? NOTE. Think that the original xy co-ordinate system has been rotated in respect to the origin so that line L defines the new x-axis x and y is the new y-axis! 6. Two cyclists drive a distance of 15 kilometres. One of the cyclists drives 10 km h faster than the other one and arrives at their destination 0 minutes earlier. What are the speeds of the cyclists? 7. In the following addition problem all As denote one digit, all Bs denote another digit and C denotes a third digit. AAA What are these digits? BBB AAAC

Part 1, section A, page 3/x Section A: PROBLEM SOLVING, MATHEMATICS: ANSWERS Problem 1: Answer a: Answer b: Answer c: 3

Part 1, section A, page 4/x Problem : Answer a: Answer b: Answer c: Problem 3: Answer a: Answer b: Answer c: 4

Part 1, section A, page 5/x Problem 4: Problem 5: Answer: Answer a: Answer b: 5

Part 1, section A, page 6/x Problem 6: Problem 7: Answer: Answer: 6

Part 1, section B, page 7/x Part 1, section B: PROBLEM SOLVING, PHYSICS The physics part of the exam consists of three (3) problems in physics. Please answer in the space reserved for each task. The main ideas of the calculations must be shown. FAMILY NAME AND FIRST NAME(S): APPLICATION NUMBER: DATE OF BIRTH: APPLICATION OPTIONS: PROBLEMS: Civil Engineering Information Technology Media Engineering 1. Consider the pictured roller coaster track. There is a roller coaster car at point B at a height of 16 m moving uphill towards point A at a speed of 10 m/s. The car has no engine, it rolls freely and all frictional forces are disregarded. Will the car go over the hill on the left and past point A, or will it go over the hill to the right past point D, or will it be restricted to move in the valley between points A and D? m Note. g 9.8 s 5 A 0 D B 15 10 m 16m C 0m 5 10m 0 3 4 5 6 7 8 9 10 11 1 13 7

Part 1, section B, page 8/x 1. The resistors in the circuit shown below are identical and each has resistance R. The terminal voltage (potential difference) of the source is E. i. Find the current I. ii. What is the potential difference V cd between points C and D expressed as a fraction of E? I E C D. Sketch the graphs of a(t) and v(t) for the following situation: Two forces, F 1 and F ( t), act on a mass m = 1.0 kg. Force F 1 is to the left in the negative x-direction and force F ( t) is to the right in the positive x-direction. F 1 is constant with a magnitude of 1.0 N whereas F ( ) has a magnitude of.0 N for the time interval 0.0 s t 5. 0 s t and drops to zero after 5.0 s. The mass is at rest at time t = 0.0 s. a) Sketch the acceleration versus time graph for the time interval 0.0 s t 15. 0 s for the mass m. There is a co-ordinate system reserved for this on the answer sheet. b) Sketch the velocity versus time graph for the same time interval for mass m. There is another co-ordinate system reserved for this on the answer sheet. F m F ( t) 1 8

Part 1, section B, page 9/x Part 1, section B: PROBLEM SOLVING, PHYSICS: ANSWERS Problem 1: Answer: Problem : Answer a: Answer b: 9

Part 1, section B, page 10/x Problem 3a: 6 4 a(m/s ) 0 - -4-6 0 5 10 15 t(s) Problem 3b: 1.5 1 0.5 v(m/s) 0-0.5-1 -1.5-0 5 10 15 t(s) 10

Part, page 1/N Part : QUESTIONS ON MOTIVATION The Questions on Motivation test consists of xxxx questions. Please read and follow the instructions below. FAMILY NAME AND FIRST NAME(S): APPLICATION NUMBER: DATE OF BIRTH: APPLICATION OPTIONS: Civil Engineering Information Technology Media Engineering Instructions: 1 Read the questions carefully and answer them briefly and to the point. Answer all the questions. 3 Write in complete sentences and use clear handwriting. 4 Write the answers in the spaces indicated on the following pages. NOTE: Due to the nature of this part of the exam, we do not provide model questions. 11

Part 3, page 1/3 Part 3: ENGLISH LANGUAGE TEST: ESSAY Start time: : The language test consists of an essay. Please read and follow the instructions below. FAMILY NAME AND FIRST NAME(S): APPLICATION NUMBER: DATE OF BIRTH: APPLICATION OPTIONS: Civil Engineering Information Technology Media Engineering Instructions for the essay: 5 Write an essay of 00-30 words on the given topic (see the following page). All words count, even articles and prepositions. Count the words and give the exact number of words at the end of the essay. 6 Write in complete sentences and use clear handwriting. Divide your text into a few paragraphs. 7 Write the essay in the space indicated on the following two pages. Please note that the essay WILL NOT BE ASSESSED IF it is shorter or longer than stated in the instructions it is not written in the space indicated in the instructions; in other words, an essay written on any other sheet will not be assessed it is not written on the given topic. NOTE: Due to the nature of this part of the exam, we do not provide model questions. 1